Consider the following attempted reductio of Anselmian theism (based on Rowe, Can God be Free?):

God exists and actualized the actual world and no being could possibly be greater than God actually is (assumption for reductio)

There is a possible world, w, which is better than the actual world (premise)

Possibly, God actualizes w (premise)

Therefore, possibly, God does better than God in fact did (from 1-3)

Therefore, possibly, God is greater than God in fact is (from 4)

The conclusion 5 of course contradicts the assumption 1. What I want to point out here is just that 5 does not follow validly from 4. That is, doing better does not logically entail being greater. This is easy to see in cases where the agents face different choices: a devil may make a better choice than a saint if the devil’s worst option is better than the saint’s best option!

Rowe’s view seems to be that, at least in cases where two agents face the same array of options, if the first does better than the second then the first is greater than the second. Thus restricted, the view has some intuitive plausibility. However, it is not clear that we should extend it to the kinds of cases where Rowe applies it, such as cases where, for every option, there is a better one. In that case, it seems quite plausible that an agent might do better without being better. For instance, compare an agent who chooses option 685 because, due to having the wrong set of values, he takes it to be the best option, with an agent who correctly realizes that there is no best option and arbitrarily selects option 500 because it is better to do something than to do nothing. The second agent seems clearly better than the first.
The moral of the story is, I think, that God’s perfect goodness should not be understood as his acting unsurpassably well. It should instead be understood as some feature of his character. Perhaps (I’m not sure) it can be cashed out in terms of God valuing every possible entity or state of affairs exactly as much as he ought. (I’m assuming that God’s perfect goodness means more than just his fulfilling any moral duties he might have.) This is a property which, when combined with the thesis that there is a BPW, would entail that God creates it, but would not have problematic consequences if there were no BPW, so I think it might line up pretty well with intuitions about the matter.
(cross-posted at blog.kennypearce.net)

Kenny:
Just adding the premise
4.1. If one acts better, one is greater
will not make the argument valid. To make the argument valid, you need a second premise:
4.2. If one brings about a better outcome, one acts better.
The examples you give are actually counterexamples to 4.2 rather than to 4.1.
And I wonder if one can’t salvage 4.2 somewhat as follows:
4.2a. If one assigns the correct values to all options, then keeping constant the array of options and the satisfaction of all imperfect role duties, if one knowingly brings about a better outcome without violating any deontic constraints, one acts better.
This would require a bunch of auxiliary premises in the argument, of course. (The imperfect role duties stuff concerns the worry that perhaps one’s role gives one imperfect duties fulfilling which could bring about a less good outcome, but fulfilling them would nonetheless make for a better act. For instance, one might think that it is better for a headachy stranger to get two Tylenols than for one’s headachy friend to get one, but if one has a choice between onerously giving one Tylenol to a headachy friend or two to a stranger, one does better to give one to one’s friend. But the because I’ve stipulated this as onerous, it’s only an imperfect duty.) And there may be further qualifications.
My own answer is incommensurability. There is no better world than this one, but there are plenty of incommensurable worlds.

Alex,
Good point about the need for 4.2, but I’m not sure whether all of my counterexamples are to 4.2 rather than 4.1. This depends, I suppose, on how one describes/individuates actions. Suppose, one has a theory of abundant actions (like abundant universals) where every non-synonymous description of what happened picks out a distinct action. Then surely some of the actions the saint performs will be worse actions (not just worse outcomes) than the actions taken by the devil.
Here, however, I’m still making an assumption which could be challenged, namely:
4.2b If one does a better action, one acts better.
At first glance this looks like a tautology, but on reflection perhaps it is not universally true, since the antecedent talks about which action one performs, and the consequent talks about the manner in which one acts, and these are not universally equivalent. To act quickly, or happily, or quietly, is not to perform some particular action, and perhaps the same is true of (for instance) acting virtuously.
In the post I used the phrase ‘do better’ rather than ‘act better,’ and ‘to do better’ in English is often an idiom meaning something like ‘to produce a better result.’ However, spelling things out this way is helpful for getting clear on the issues.

The multiplicity of actions point is a good one, even in a sparse theory, since even on sparse theories, typical agents perform multiple actions!
So, we’ll need some principle like:
4.2c. If there is a bijection f between the actions of x and the actions of y, such that f(A) is at least as good as A for every action A of x and f(A) is better than A for some action A of x, then y is greater (in respect of action) than x.
But 4.2c is false in the case of agents who perform an infinite number of actions. For suppose that Sam is omnitemporally eternal, and each year performs exactly one action. Moreover, each year’s action is better than the preceding year’s action. Then there is a bijection f between x’s actions and x’s actions satisfying the provisions of 4.2c. Just let f(A) = the action committed in the year after A is committed.

Alex,
You say your response to Rowe’s argument is incommensurability. Have you written about this or expanded on this point anywhere?
Kenny,
Could Rowe bypass concerns about whether doing better entails being greater by arguing that, if there is a possible world, w, which is better than the actual world, then there is a possible being, S, whose character is such that S necessarily actualizes w? S would thus not simply do better, but would in fact be greater.

Kenny,
Consider your agent who arbitrarily selects option 500 because it is better to do something than nothing, but there is no best world. Imagine that the difference between option 500 and option 600 is an act (or acts) of supererogation on the part of the agent who selects the world. Perhaps it is the atonement, or an abundance of undeserved blessings bestowed upon the creatures in those worlds. Does your proposal here force you to say that a being whose character is such that he necessarily performs such supererogatory acts is not morally superior to the character of a being who is capable of refraining from performing such acts?

Yes, and that seems right to me, insofar as the agent who necessarily chooses option 600 (a) cannot choose the better option 601, and (b) choose option 600 either unfreely (because of some kind of compulsion) or else for bad reasons (because he thinks 600 is the best).

Ah, I guess I was not very careful in how I set this up. I intended for the agent who actualized world 600 to be a being whose character required that he actualize a world no worse than 600 (600 and above would be options for him). Assuming that world 600 is morally superior to 500 (e.g. because it includes acts of supererogation like those I described), it is hard to see how a being whose character permitted selecting worlds as low as 500 is not itself morally inferior to a being whose character is such that he must select worlds at least as good as 600. If you grant me that world 600 is morally superior to world 500, and if we suppose that these agents’ moral characters are correlated with these worlds in the way I have described, why doesn’t that moral difference between the worlds transfer to the characters of these agents?
What you said in your last post under (b) shows that considerations other than character can affect the greatness of a being (your points there were about the knowledge and freedom of the agent who chooses 600, not his character per se). But if we bracket these other properties and put aside the question of which being is greater overall, wouldn’t it still be true that the being who must select 600 or better has a superior moral character to the being who must select 500 or better?

I don’t think so. I think the (morally) best being would value each of its options (and the states of affairs it believes those options would bring about) correctly, and be appropriately moved by those considerations. I don’t think adding a ‘cutoff’ at a morally arbitrary point makes a being better. This is just an intuition; I don’t really have a theory.